{"title":"通过弗斯滕伯格族实现超空间和积系统中的敏感性","authors":"Arpit Mahajan , Rahul Thakur , Ruchi Das","doi":"10.1016/j.topol.2024.108907","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we study the notions of <span><math><mi>F</mi></math></span>-sensitivity, multi-<span><math><mi>F</mi></math></span>-sensitivity and <span><math><mo>(</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span>-sensitivity in dynamical systems defined on Hausdorff uniform spaces. It is shown that how these notions carry over to hyperspatial and product dynamical systems, and vice versa. We also obtain some sufficient conditions for a dynamical system to be <span><math><mi>F</mi></math></span>-sensitive. Some examples showing the necessity of the conditions taken in our results are also presented.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Sensitivity in hyperspatial and product systems via Furstenberg families\",\"authors\":\"Arpit Mahajan , Rahul Thakur , Ruchi Das\",\"doi\":\"10.1016/j.topol.2024.108907\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we study the notions of <span><math><mi>F</mi></math></span>-sensitivity, multi-<span><math><mi>F</mi></math></span>-sensitivity and <span><math><mo>(</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span>-sensitivity in dynamical systems defined on Hausdorff uniform spaces. It is shown that how these notions carry over to hyperspatial and product dynamical systems, and vice versa. We also obtain some sufficient conditions for a dynamical system to be <span><math><mi>F</mi></math></span>-sensitive. Some examples showing the necessity of the conditions taken in our results are also presented.</p></div>\",\"PeriodicalId\":51201,\"journal\":{\"name\":\"Topology and its Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-04-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Topology and its Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0166864124000920\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Topology and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0166864124000920","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
本文研究了定义在豪斯多夫均匀空间上的动力系统中的 F 敏感性、多 F 敏感性和 (F1,F2) 敏感性概念。结果表明，这些概念如何应用于超空间和积动力系统，反之亦然。我们还得到了动力学系统对 F 敏感的一些充分条件。我们还举例说明了我们的结果中所采用的条件的必要性。
Sensitivity in hyperspatial and product systems via Furstenberg families
In this paper, we study the notions of -sensitivity, multi--sensitivity and -sensitivity in dynamical systems defined on Hausdorff uniform spaces. It is shown that how these notions carry over to hyperspatial and product dynamical systems, and vice versa. We also obtain some sufficient conditions for a dynamical system to be -sensitive. Some examples showing the necessity of the conditions taken in our results are also presented.
期刊介绍：
Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology.
At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.
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